Observing the bouncing of a marble on a table is a rather common experience. The tic-tac sound of the rigid ball, nevertheless, carries quite a pleasant surprise. In fact, by measuring the total time of bouncing Δt, the coefficient of restitution can be estimated. As is well known, in an inelastic collision the kinetic energy is not conserved, and therefore the speed decreases. The speeds vi and vf, before and after the collision occurs, respectively, are related as follows: ν_f=ε ν_i, (1) where ε &lt; 1. By measuring the initial height h0 from which the marble is released, we find that ε={T−sqrt{2h_0g}}over{T+sqrt{2h_0g}}, (2) where g is the acceleration due to gravity and T is the total time from initial release until the ball stops bouncing.

Bouncing Balls and Geometric Progressions

Abstract

Observing the bouncing of a marble on a table is a rather common experience. The tic-tac sound of the rigid ball, nevertheless, carries quite a pleasant surprise. In fact, by measuring the total time of bouncing Δt, the coefficient of restitution can be estimated. As is well known, in an inelastic collision the kinetic energy is not conserved, and therefore the speed decreases. The speeds vi and vf, before and after the collision occurs, respectively, are related as follows: ν_f=ε ν_i, (1) where ε < 1. By measuring the initial height h0 from which the marble is released, we find that ε={T−sqrt{2h_0g}}over{T+sqrt{2h_0g}}, (2) where g is the acceleration due to gravity and T is the total time from initial release until the ball stops bouncing.
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2020
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11386/4750670`
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